Box Center - (0.25, 0.25, 0.00)
Box Side Length - (2.00, 1.50, 1.50)

Note : No View Dependence

Algorithm :

1. Initialize a set of points for all rays with origin
2. Iterate (for max_iters):
   1. Find Distance To Collisison at all points
   2. Update points by adding the distance (SDF value) in the ray direction
3. Apply a threshold to distance (SDF Value) for all updated points, to get mask

Code Implementation :

    def sphere_tracing(self, implicit_fn,
	     origins, # Nx3
        directions, # Nx3
    ):        
        points = origins
        for i in range(self.max_iters):
            distance = implicit_fn(points)
            points = points + directions * distance
        
        mask = implicit_fn(points) < 1
        return points, mask
Copy

Best Results (alpha = 10, beta = 0.05)

Hyperparameter Tuning --
Changing alpha, (beta = 0.05) -

Changing beta, (alpha = 10) -

Analysis -

1. How does high beta bias your learned SDF? What about low beta?
   High Beta -> smoother and diffused surface
   Low Beta -> sharper surface with jagged edges

2. Which beta value is better for training with volume rendering?
   High Beta.
   Reason - higher beta leads to a smoother and broader surface leading to a higher overlap with the true surface helping the optimization convergence.
   Lower beta might cause overfitting risks and unstable gradients making training difficult.

3. Would you be more likely to learn an accurate surface with high beta or low beta? Why?
   Low beta helps in capturing sharp edges and fine details, thus making it better for learning a very accurate surface.

8.2 Fewer Training Views